No, only the first one is correct. Some other adverbs of frequency (like "sometimes") could also go at the beginning or end of the sentence, but "never" and "always" need to go just before the verb.

#3 is not correct, but #4: "Never am I late for work" is excellent. The problem with #3 is that it separates the adverb "never" from the word that it modifies ("late"). "Never" likes to be next to the word it modifies. #4 works because "never" is next to the word it modifies, which is "am". So #1 and #4 are quite different. #1 speaks of "never late", while #4 speaks of "never am".